In China, new-energy vehicles are viewed as the ultimate goal for the automobile industry, given the current focus on the “dual-carbon” target. Therefore, it is important to promote the sustainable development of this new-energy market and ensure a smooth transition from fuel-driven vehicles to new-energy vehicles. This study constructs a tripartite evolutionary game model involving vehicle enterprises, consumers, and the government. It improves the tripartite evolutionary game through the mechanisms of dynamic and static rewards and punishments, respectively, using real-world data. The results show the following. (1) A fluctuation is present in the sales of new-energy vehicles by enterprises and the active promotional behavior of the government. This fluctuation leads to instability, and the behavior is difficult to accurately predict, which is not conducive new-energy vehicles’ promotion and sales. (2) A static reward and punishment mechanism can change the fluctuation threshold or peak value. Nevertheless, the stability of the system’s strategy is not the main reason that the government has been actively promoting it for a long time. However, enterprises are still wavering between new-energy and fuel vehicles. (3) The linear dynamic reward and punishment mechanism also has its defects. Although they are considered the stability control strategy of the system, they are still not conducive to stability. (4) The nonlinear dynamic reward and punishment mechanism can help the system to achieve the ideal stabilization strategy.